A community in a network is a group of vertices such that there is a higher density of edges within the group than between them.

Given a graph , let the vertex set be partitioned into subsets such that each subset belongs to one community. The community modularity of this partition is defined as
, where is the percentage of edges that have both ends in community , and is the percentage of edges that start from community . In other words,
and .

The community modularityis a number less than or equal to 1. A large positive value indicates that the vertex partition gives significant community structure.